Least Common Multiple (LCM) of 114 and 138
The least common multiple (LCM) of 114 and 138 is 2622.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 114 and 138?
First, calculate the GCD of 114 and 138 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 138 = 0 remainder 114 |
| 2 | 138 ÷ 114 = 1 remainder 24 |
| 3 | 114 ÷ 24 = 4 remainder 18 |
| 4 | 24 ÷ 18 = 1 remainder 6 |
| 5 | 18 ÷ 6 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 84 and 37 | 3108 |
| 38 and 14 | 266 |
| 96 and 171 | 5472 |
| 198 and 62 | 6138 |
| 46 and 194 | 4462 |